MinT - Best Known (157−44, 157, s)-Nets in Base 8

Best Known (157−44, 157, s)-Nets in Base 8

(157−44, 157, 1026)-Net over F₈ — Constructive and digital

Digital (113, 157, 1026)-net over F₈, using

13 times m-reduction [i] based on digital (113, 170, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 85, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(157−44, 157, 4804)-Net over F₈ — Digital

Digital (113, 157, 4804)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−44, 157, 3601901)-Net in Base 8 — Upper bound on s

There is no (113, 157, 3601902)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6097 167281 578508 565127 133873 610944 862797 362091 906670 978263 863059 572195 484083 749478 311980 685016 543017 795017 176098 061566 917465 492887 320333 051976 > 8¹⁵⁷ [i]